Goal: Understand the sampling approach
Goal: Identify a sampling distribution for the data
Goal: Examine the spatial pattern of the response
Explore the code below: what are the differences in the three variograms?
coordinates(scallop) = ~longitude+latitude
class(scallop)
scallop.sp <- scallop
proj4string(scallop.sp) <- CRS("+proj=longlat +datum=WGS84")
scallop.utm <- spTransform(scallop.sp, CRS("+proj=utm +zone=18 ellps=WGS84"))
plot(variogram(log.catch~1, scallop))
plot(variogram(log.catch~1, scallop.sp))
plot(variogram(log.catch~1, scallop.utm))Goal: Visually diagnose spatial structure
Goal: Determine if direction influencs spatial structure
If the differences in spatial structure are directly related to two coordinate sets, we can create a stationary, anistropic covariance function
A scaling factor, \(\sigma^2,\) can be used to create covariance.
dist.mat <- dist(coords, diag = T, upper = T) %>% as.matrix()This requires a distributional assumption, we will use the Gaussian distribution
What about the rest of the locations on the map?
How does the spatial process change with: